Spectra and gap amplification for systems with two widely different incommensurate periodicities

M. Ya Azbel, Per Bak, P. M. Chaikin

    Research output: Contribution to journalArticle

    Abstract

    We derive analytically the spectrum for the Schrödinger equation for quasiperiodic systems with two length scales: one large macroscopic scale [e.g., a cos(2x/≫)] and one small microscopic scale [e.g., v cos(2x)]. The phase diagram includes regimes with exponentially narrow gaps due to the slowly varying potential, regimes where the rapidly varying potential amplifies these narrow gaps, and regimes with exponentially narrow Landau bands. The full devils-staircase spectrum with gaps at wave vectors q=mn/≫ develops in a hierarchical manner as a increases. The results apply to systems with superlattices, to celestial orbits with two periodic perturbations, to systems with slowly varying lattice distortions, and, in particular, to quasi-one-dimensional magnets such as bis(tetramethyltetraselenafulvalene) perchlorate [(TMTSF)2ClO4] in magnetic fields, where our findings may provide insight into the experimentally observed cascade of phase transitions.

    Original languageEnglish (US)
    Pages (from-to)1392-1402
    Number of pages11
    JournalPhysical Review A
    Volume34
    Issue number2
    DOIs
    StatePublished - 1986

    Fingerprint

    periodic variations
    stairways
    perchlorates
    superlattices
    cascades
    magnets
    phase diagrams
    orbits
    perturbation
    magnetic fields

    ASJC Scopus subject areas

    • Physics and Astronomy(all)
    • Atomic and Molecular Physics, and Optics

    Cite this

    Spectra and gap amplification for systems with two widely different incommensurate periodicities. / Azbel, M. Ya; Bak, Per; Chaikin, P. M.

    In: Physical Review A, Vol. 34, No. 2, 1986, p. 1392-1402.

    Research output: Contribution to journalArticle

    Azbel, M. Ya ; Bak, Per ; Chaikin, P. M. / Spectra and gap amplification for systems with two widely different incommensurate periodicities. In: Physical Review A. 1986 ; Vol. 34, No. 2. pp. 1392-1402.
    @article{50d6dc0e14654fdc9bad718ce6c83014,
    title = "Spectra and gap amplification for systems with two widely different incommensurate periodicities",
    abstract = "We derive analytically the spectrum for the Schr{\"o}dinger equation for quasiperiodic systems with two length scales: one large macroscopic scale [e.g., a cos(2x/≫)] and one small microscopic scale [e.g., v cos(2x)]. The phase diagram includes regimes with exponentially narrow gaps due to the slowly varying potential, regimes where the rapidly varying potential amplifies these narrow gaps, and regimes with exponentially narrow Landau bands. The full devils-staircase spectrum with gaps at wave vectors q=mn/≫ develops in a hierarchical manner as a increases. The results apply to systems with superlattices, to celestial orbits with two periodic perturbations, to systems with slowly varying lattice distortions, and, in particular, to quasi-one-dimensional magnets such as bis(tetramethyltetraselenafulvalene) perchlorate [(TMTSF)2ClO4] in magnetic fields, where our findings may provide insight into the experimentally observed cascade of phase transitions.",
    author = "Azbel, {M. Ya} and Per Bak and Chaikin, {P. M.}",
    year = "1986",
    doi = "10.1103/PhysRevA.34.1392",
    language = "English (US)",
    volume = "34",
    pages = "1392--1402",
    journal = "Physical Review A",
    issn = "2469-9926",
    publisher = "American Physical Society",
    number = "2",

    }

    TY - JOUR

    T1 - Spectra and gap amplification for systems with two widely different incommensurate periodicities

    AU - Azbel, M. Ya

    AU - Bak, Per

    AU - Chaikin, P. M.

    PY - 1986

    Y1 - 1986

    N2 - We derive analytically the spectrum for the Schrödinger equation for quasiperiodic systems with two length scales: one large macroscopic scale [e.g., a cos(2x/≫)] and one small microscopic scale [e.g., v cos(2x)]. The phase diagram includes regimes with exponentially narrow gaps due to the slowly varying potential, regimes where the rapidly varying potential amplifies these narrow gaps, and regimes with exponentially narrow Landau bands. The full devils-staircase spectrum with gaps at wave vectors q=mn/≫ develops in a hierarchical manner as a increases. The results apply to systems with superlattices, to celestial orbits with two periodic perturbations, to systems with slowly varying lattice distortions, and, in particular, to quasi-one-dimensional magnets such as bis(tetramethyltetraselenafulvalene) perchlorate [(TMTSF)2ClO4] in magnetic fields, where our findings may provide insight into the experimentally observed cascade of phase transitions.

    AB - We derive analytically the spectrum for the Schrödinger equation for quasiperiodic systems with two length scales: one large macroscopic scale [e.g., a cos(2x/≫)] and one small microscopic scale [e.g., v cos(2x)]. The phase diagram includes regimes with exponentially narrow gaps due to the slowly varying potential, regimes where the rapidly varying potential amplifies these narrow gaps, and regimes with exponentially narrow Landau bands. The full devils-staircase spectrum with gaps at wave vectors q=mn/≫ develops in a hierarchical manner as a increases. The results apply to systems with superlattices, to celestial orbits with two periodic perturbations, to systems with slowly varying lattice distortions, and, in particular, to quasi-one-dimensional magnets such as bis(tetramethyltetraselenafulvalene) perchlorate [(TMTSF)2ClO4] in magnetic fields, where our findings may provide insight into the experimentally observed cascade of phase transitions.

    UR - http://www.scopus.com/inward/record.url?scp=35949025839&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=35949025839&partnerID=8YFLogxK

    U2 - 10.1103/PhysRevA.34.1392

    DO - 10.1103/PhysRevA.34.1392

    M3 - Article

    VL - 34

    SP - 1392

    EP - 1402

    JO - Physical Review A

    JF - Physical Review A

    SN - 2469-9926

    IS - 2

    ER -